Constrictivity is a dimensionless parameter used to describe transport processes (often

molecular diffusion Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of ...

) in

porous media A porous medium or a porous material is a material containing pores (voids). The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid (liquid or gas). The skeletal material is usu ...

. Constrictivity is viewed to depend on the ratio of the diameter of the diffusing

particle In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object which can be described by several physical property, physical or chemical property, chemical ...

to the pore diameter. The value of constrictivity is always less than 1. The constrictivity is defined not for a single pore, but as the parameter of the entire pore space considered. The resistance to transport in porous media increases because the

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

of the fluid (which fills the pores) increases in the vicinity of the pore walls (Renkin effect;Renkin, EM (1954): ''Filtration, diffusion and molecular sieving through porous cellulose membranes.'' J. Gen. Physiologist., 38: 225-243 see also

electroviscous effects Electroviscous effects, in chemistry of colloids and surface chemistry, according to an IUPAC definition, are the effects of the particle surface charge on viscosity of a fluid. Viscoelectric is an effect by which an electric field near a charged ...

). This effect is important in very narrow pores and in pore narrowing their diameter to the same size as the diameter of the diffusing particles. Constrictivity must be distinguished from the effects of

Knudsen diffusion In physics, Knudsen diffusion, named after Martin Knudsen, is a means of diffusion that occurs when the scale length of a system is comparable to or smaller than the mean free path of the particles involved. An example of this is in a long pore wi ...

. Knudsen diffusion occurs when the particle interacts with the pore walls more than it does with other particles due to the large free path and narrow pores. Constrictivity, on the other hand, depends on the influence of the pore walls on the fluid filling the pores. There are a number of empirical formulas used to estimate the value of constrictivity. For simple pore geometries, constrictivity can be inferred from the geometry of the porous media.Michaels, AS (1959): ''Diffusion in a pore of irregular cross section.'' AIChE J., 5: 270-271 In practice, the constrictivity together with the

porosity Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure ...

and

tortuosity Tortuosity is widely used as a critical parameter to predict transport properties of porous media, such as rocks and soils. But unlike other standard microstructural properties, the concept of tortuosity is vague with multiple definitions and vari ...

are often used in models as purely empirical parameters to establish the effective diffusivities in porous media.

Footnotes

Sources

*P. Grathwohl: ''Diffusion in natural porous media: Contaminant transport, sorption/desorption and dissolution kinetics''. Kluwer Academic Publishers, 1998, *R. K. M. Thambynayagam: ''The Diffusion Handbook: Applied Solutions for Engineers''. McGraw-Hill, 2011, *van Brakel, J., Heertjes, P. M. (1974): ''Analysis of diffusion in macroporous media in terms of a porosity, a tortuosity and a constrictivity factor.'' Int. J. Heat Mass Transfer, 17: 1093–1103 Porous media Transport phenomena Hydrogeology {{materials-sci-stub